The Liar's paradox

Discussion in 'General Philosophy' started by Speakpigeon, Feb 6, 2019.

  1. Quantum Quack Life's a tease... Valued Senior Member

    Messages:
    23,277
    there is no point to explaining something that is way over your head. I tried and I failed. Perhaps you could attempt to explain the difference between :
    1-1 = 0
    and
    0=1-1
    and demonstrate an ability to offer criticism of others work.

    with out zero any number becomes a floating variable....zero is the anchor that provides constancy of value.
    1=1 because
    1-1 = 0
    0=0 because
    0-0 = 0
    not
    0= 1-1

    Mathematics is a branch of philosophy so exactly who is being idiotic?
    because as stated earlier nothingness or zero is fundamentally important to achieving and maintaining constancy of value. The non-existence that zero implies, is fundamental to mathematical integrity.
    The only "thing" that is universally constant (in absolutuum) in all of mathematics is zero. If zero was in any way floating in value, mathematics would be scrambled egg....


    So....
    do some head work and compare:
    0= x + (-)x
    with the famous "ex-nihilo" paradox and see how you go...

    then apply what you learn to your liars paradox...

    Go on... "slay the ego" ... and get some credit on the board
     
    Last edited: Feb 11, 2019
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  3. Speakpigeon Valued Senior Member

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    You haven't explained anything. It seems rather plain you're unable to explain the rather fuzzy statements you favour.
    I already told you, I don't understand.
    And you're clearly unable to explain.
    You think a horse is a horse because...???
    Why not?
    You.
    Why?
    That may be how you feel about it but you still have to explain how that would be intrinsic to mathematics (as opposed to intrinsic to your own philosophical "theory").
    You seem to interpret the sign "=" as signifying the allocation or assignment of a value. You think "x = 2" means the value 2 is affected to x, i.e. like the operator ":=" in software programmes. Interesting.
    In mathematics, the sign "=" means equality. Equality is a relation, not an operation. And it's a symmetrical relation so that "x = 0 "is equivalent to "0 = x".
    So, I really don't see how there could be any problem in that intrinsic to mathematics (as opposed to intrinsic to your own philosophical "theory").
    Well, I don't understand what you're trying to say. You're not explaining anything. You point your finger at two equalities that are equivalent and you just suggest they are not equivalent... Beats me.
    And you are the expert here, so apply your expertise.
    EB
     
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  5. iceaura Valued Senior Member

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    30,994
    Or truth and falsehood, then, in any mathematically rigorous sense.
    As you insisted, earlier, it's a sentence.
    One could discuss its meaning, but you are not interested.
    So:
    Grey-green, medium saturation, is my proposal.
     
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  7. Quantum Quack Life's a tease... Valued Senior Member

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    Understanding the nature of the liars paradox requires dealing with the nuances of the logic involved. The liars paradox can be, I believe, mathematically described ( explained ) if one cares to attempt to understand the explanation by using the following mathematical arrangement:
    Unfortunately symbols used for logic are not easily generated by fora software, I can't remember the code and I don't think is would be understood here any how.

    As Write4U correctly surmised in an earlier post:

    x + (-)x = 0 =/= (-)x + x
    On the left side of our central subject zero the formation is relative to zero.
    On the right side of the central subject zero the formation the relationship is absolute.

    When taking in the entire formation simultaneously ( not left to right but middle outwards) there is a relative vs absolute zero paradox.

    This sentence is false, is worded as such that it can only be taken as a whole and not read left to right.

    this sentence = (false+true) = this sentence.

    or by substitution:

    this sentence = 0 =/= this sentence

    Zero is both relative ( false ) and absolute (true)
    thus
    x + (-)x = relative zero
    where as
    absolute zero =/= x + (-)x

    so...
    x + (-)x = 0 =/= (-)x + x

    is the best way I know of when attempting to explain the nature of a paradox.

    Remember that in philosophy it is generally accepted that "nothing" is absolutely (objectively) true, that is to say objective truth is unavailable to the human mind. (ego)

    Yet "nothing" can also be a relative concept and deliver the subjective truth.

    Just like zero can have infinite dimension and zero dimension simultaneously.

    Ex nihilo is the same issue:
    and can be described as 0 = x + (-)x (which is false btw)
    and I might add ultimately solved in the same manner...

    and you can send me your cheque later.....

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    Note: the use of the symbol =/= denotes "not equal to"
     
    Last edited: Feb 12, 2019
  8. Baldeee Valued Senior Member

    Messages:
    2,121
    QQ, I am not sure you are explaining yourself adequately, or that mathematics is the best language to express what you are trying to explain, and your attempts to do so just come across as... muddled.
    For example, you say that x + (-)x = 0 is not equal to (-)x + x when in mathematics it very much is equal to.
    This is due to the cumulative property of addition, and the inverse property of addition.

    Whenever you see x + (-)x this is always the equivalent of, and equal to, zero.
    It doesn't matter if you intend to use it as such or not.
    This is the inverse property of addition: anything plus its negative sums to zero.

    Similarly whenever you see a + b this is identical to b + a.
    This is referred to as the cumulative property of addition.

    x + (-)x is therefore identical to, due to the cumulative property of addition, (-)x + x.
    And due to the additive inverse property, both are equal to zero.

    Thus when you say the two are not equal, this is incorrect.

    Now maybe you are trying to explain something different, and if so then perhaps mathematics is really not the best language for it.
    But currently your argument/explanation is being lost as it seems to go against the very properties of mathematics that make it what it is.
     
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  9. Quantum Quack Life's a tease... Valued Senior Member

    Messages:
    23,277
    Thanks for posting. It is true as you say that mathematics has significant difficulty when dealing with paradoxes and yes, borrowing a language not fit for purpose is not the best.
    To demonstrate a paradox as a reality using language that can not allow such is bound to be frustrating. So pushing the boundaries I am.
    A quick Google and...
    So in summary, a paradox cannot exist in a given body of logic unless it is the trivial one. Since humans tend not to believe that every statement is true, we believe that there are no paradoxes in our reality. ...

    generally sets the attitude....
    as incorrect as it is IMO
    Ask me:
    Am I aware of or know of any real, measurable, consistent physical paradoxes in reality?
    My answer would be yes, but putting it in a mathematical form is, or at least appears to be, impossible with out manipulating or bending the rules. And I am no mathematician....
     
    Last edited: Feb 12, 2019
  10. Quantum Quack Life's a tease... Valued Senior Member

    Messages:
    23,277
    btw if I accepted that equivalence is always symmetrical I wouldn't use mathematics to describe a paradox.
    By using the form:
    x + (-)x = 0 =/= (-)x + x
    I am demonstrating that a paradox can only be described when that fundamental of math ( the reciprocation of equivalence) is challenged with regards to zero.
    If I simply wrote:
    x + (-)x = 0 = (-)x + x
    I certainly would not be describing a paradox... yes?
    The main point is that for a paradox to exist it MUST break the reciprocal symmetry of equivalence.
     
  11. Baldeee Valued Senior Member

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    2,121
    Can you name one "real, measurable, consistent physical paradox" that exists in reality?
    My take on paradoxes is that none can possibly exist in reality.
    Anything real that might appear to be paradoxical only seems that way due to our lack of understanding.
    If something appears paradoxical then it is an indication that our understanding of reality is not sufficient.
    But please provide an example of what you think is a paradox that exists in reality?
     
  12. Quantum Quack Life's a tease... Valued Senior Member

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    23,277
    Briefly,
    The issue can be demonstrated by the following question:

    To avoid escape velocity [therefore continuous acceleration] when velocity of an object is sustained as steady away from a source of attraction, what counter forces to the source of attraction are required?

    You will find that the forces counter to attraction forces have to be reduced as the distance from source of attraction increases. Leading to a scalloping effect.

    So more energy required to get to a position that requires less energy is the paradox...thus maintaining a velocity as steady away from a source of attraction is impossible.

    Try moving a piece of iron away from a magnet with your hand at a steady rate and see how impossible this is.
     
  13. Quantum Quack Life's a tease... Valued Senior Member

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    23,277
    So... if you wanted to do the mathematics required for the applied energy of a steady and non accelerating velocity climb into orbit you would find it impossible. ( ignoring the initial starting acceleration from v=0)
     
    Last edited: Feb 12, 2019
  14. Baldeee Valued Senior Member

    Messages:
    2,121
    Eh?
    What does "to avoid escape velocity" mean?

    The answer to the question is that to travel away from a source of attraction you need to apply thrust, and the level of thrust would need to follow a continuous time-related function.
    It is possible, and it is not a paradox.
    If you only make adjustments to the thrust at specific intervals then yes, it would not be possible.
    But not being possible also does not make it a paradox.

    The maths of the situation I think you are describing is known.
    There is simply nothing paradoxical about it.
    Why do you think there is?
    What is paradoxical about the scenario?
     
  15. Quantum Quack Life's a tease... Valued Senior Member

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    23,277
    yes you have to apply thrust in a constantly reducing manner as you move away from the source of attraction. However while you have to increase your thrust to move upwards, you have to decrease your thrust as soon as you do....ie. stronger but weaker.

    ...because if you just decrease your thrust you'll fall and not climb, and you have constant acceleration towards the source of attraction. (and vice versa.)

    I believe the paradox is a natural outcome of the inverse square or cube rules.

    Try graphing the thrust required to achieve a non-accelerating, steady velocity outcome in either direction in an intense field of attraction and you will see that it is impossible with out acceleration and de-acceleration - scalloping.

    Field of attraction


    source ------------------------position A ----------> position B------------------------------
    Stronger---------------------------------------------------------------------------------Weaker
     
    Last edited: Feb 12, 2019
  16. Quantum Quack Life's a tease... Valued Senior Member

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    23,277
    I did a bit of digging around in my files from way back and found this to describe the scalloping or wave effect generated. (image created :2014)
    Moving from position A to B over an infinitesimal distance with in a reducing field of attraction.

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    and yes I am fully aware of just how controversial such a claim may be...

    IMO it is up to Mathematics to evolve to deal with this reality .....as it simply can't handle it at the moment.
     
    Last edited: Feb 12, 2019
  17. Baldeee Valued Senior Member

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    2,121
    It can handle it really quite well, actually.
    And it's also really quite simple.
    Once you have obtained your desired velocity, your thrust up simply has to equal the force of gravity so that the net acceleration is zero (notwithstanding air friction).
    And we have known how to calculate such things as the force due to gravity, since Newton in fact.
    Calculus can take care of the rest in that you derive a formula for the rate of change of thrust with respect to time.
    Long gone is the need to consider discrete blocks.

    No paradox, QQ.
    Just maths.
     
  18. Quantum Quack Life's a tease... Valued Senior Member

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    23,277
    well.... show it...
    where is the math?
    link perhaps?
    Remember we are discussing things in absolute terms... Heisenberg comes close, as does Maxwell but they are not quite on the nail IMO.
    Facts:
    An object can not move away from a source of attraction by applying less energy.
    You have to apply more energy to move into a position requiring less energy.

    ...a more+less paradox exists if you seek a steady, non-accelerating velocity away from a source of attraction. This is forced upon us as an outcome of the inverse laws.
     
    Last edited: Feb 13, 2019
  19. Quantum Quack Life's a tease... Valued Senior Member

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    23,277
    You need to look deeper... because gravitational attraction is reducing constantly as you move further away from source. True, a relatively stable velocity can be computed but this is not the same as an absolutely stable velocity.

    No matter how well you compute it the end result would include a wave profile for the movement as indicated in the diagram I posted:

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  20. James R Just this guy, you know? Staff Member

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    37,110
    It is a paradox, and there's no solution.

    Should?

    You're asking us to make some kind of moral judgment about the possibility of a logical proof? Seems a bit odd.
     
  21. James R Just this guy, you know? Staff Member

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    37,110
    What are you talking about? Both sides of your two equations evaluate to zero. There's nothing here that says that zero is anything other than zero.
     
  22. James R Just this guy, you know? Staff Member

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    37,110
    Is this how you usually speak to women, lovey?
     
  23. James R Just this guy, you know? Staff Member

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    You're confusing the mathematical use of the symbol "=" to indicate equality, and the use of "=" in computer programming to designate an assignment operation. That is, in the computer language, a statement like "A=A+1" is interpreted as "Evaluate the expression A+1, using the current value of the variable A, then assign the result (=) to the variable A."

    If you're in doubt about this, try writing your computer program as "A+1=A". It will most likely generate an error on interpretation or compilation because the computer doesn't know what to do with the expression "A+1" on the left-hand side of the "=" sign.
     
    Last edited: Feb 13, 2019

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